When I was in undergraduate classes, I was advised to perform test of normality and equality of variance prior performing any test for means comparison (ANOVA) in the case of parametric test. However, I recently read on a paper that, normality is applied on residuals and not on measured variables.
I wish to know what is advisable if I want to publish my results in a paper. Statistically talking, is it fair to perform Normality test on residuals instead of measured variables?
Thank you very much.
Evans, E.
Hello Evans. The trouble with testing for normality of the residuals is that normality is most important when the sample size is small, and becomes less and less important as the sample size increases (see slide 9 of the file linked below, for example). Your test of normality, on the other hand, has very low power when n is small and too much power as n becomes large. So tests of normality are just not very helpful. And notice, by the way, that normality of the errors is a sufficient, but not a necessary condition. It is the sampling distributions of the regression parameters that must be (approximately) normal for valid inference in OLS models. HTH.
https://sites.google.com/a/lakeheadu.ca/bweaver/Home/statistics/files/OLS_regression_assumptions_Wooldridge.pdf
Hi, Evans,
The residuals! :-)
https://stats.stackexchange.com/questions/6350/anova-assumption-normality-normal-distribution-of-residuals
https://www.theanalysisfactor.com/the-distribution-of-dependent-variables/
Hello Evans. The trouble with testing for normality of the residuals is that normality is most important when the sample size is small, and becomes less and less important as the sample size increases (see slide 9 of the file linked below, for example). Your test of normality, on the other hand, has very low power when n is small and too much power as n becomes large. So tests of normality are just not very helpful. And notice, by the way, that normality of the errors is a sufficient, but not a necessary condition. It is the sampling distributions of the regression parameters that must be (approximately) normal for valid inference in OLS models. HTH.
https://sites.google.com/a/lakeheadu.ca/bweaver/Home/statistics/files/OLS_regression_assumptions_Wooldridge.pdf
Hello Evans,
in addition to what has been said already: You usually test your residuals because (ideally) they do not depend on the treatment (--> independence of residuals) and can therefore be tested as a whole. If you wanted to do that for your actually data, you would need to do that for each condition you specify individually, because you expect the data to be systematically biased between conditions (--> the effect of your treatment/intervention).
Other than that I agree with Bruce Weaver testing for/against normal distribution is a critical thing to do. I would always recommend to additonally rely on histograms and common sense to judge normality of your data.
Best,
Steffen
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